Numerical modeling in Chebyshev collocation methods applied to stability analysis of convection problems

An example of a high order method (Chebyshev collocation) applied to the st udy of a bifurcation problem in three dimensions is presented. The non-line ar basic equations are solved by an iterative technique. The first contribu tion to the solution is obtained using a low-order finite difference scheme while corrective terms are obtained through collocation. The bifurcation t hresholds are calculated through the perturbation equations. We study the c onvergence of the collocation method comparing different expansions. The po lynomials and their derivatives have been evaluated a priori at the colloca tion points instead of using the differentiation operators on those points. This procedure simplifies the implementation, (C) 2000 IMACS. Published by Elsevier Science B.V. All rights resented.